Continuity mistake: In the park with the water riddle, just before they argue about Zeus being a racist, you see both jugs. The 3 gallon jug is empty and the 5 gallon is possibly 3 gallons full. Then they argue. By the end of the argument, John says that the 3 gallon jug is exactly 2 gallons full and you see that the 5 gallon jug is full up, giving them the answer to the riddle.
Continuity mistake: When McClane is entering the subway, a man in a suit and a blond woman in a red dress pass behind him twice.
Continuity mistake: When they first start with the gold operation, Targo jumps on a large orange vehicle with some kind of drill on the front, already raised into the vertical position. He then jumps off and in the very next shot the drill raises from a horizontal to vertical position.
Visible crew/equipment: At the very end of the scene where McClane and Zeus take the businessman's car, just before the scene cuts, the boom mic can be seen reflected in the yellow car's back window as it is lowered, waiting for the "cut."
Factual error: The entire plot is based on the idea that they're going to steal $140 billion worth of gold. At a gold price of $300/ounce, that's 14,500 tons of gold - how's the suspension on those dump trucks? There's no way trucks like those could carry over 1,000 tonnes each, but Simon tells McClain there is $13 billion worth of gold in the back of McClain's truck.
Continuity mistake: In the beginning, when the big explosion occurs, watch the 2 last shots. Close shot from two blocks away: Big traffic jam. Wide shot from above: Half of the cars have disappeared from the same spot.
Revealing mistake: When fighting with Targo on the boat, McClane pulls a chain, which trips Targo over. When we see Targo being tripped from above, you can see it is a stunt double - not only is he bigger than the actor playing Targo, but also his hair is grey unlike Targo's brown.
Factual error: The security guard at the vault door fires a few shots from his handgun (about 6) down the hall towards Simon and the other terrorists. He then loads one of the shotguns and calls for help. After finding that the front guard was a terrorist he fires 14-15 rounds from the same shotgun before he is killed. The problem is that it was a Remington 870. Like most shotguns that size they only hold 8 rounds, or 9 if one is chambered.
Factual error: Typical for action movies. Willis and Samuel L. Jackson couldn't have possible survived the explosion of the ship being in the water or not. If the heat didn't get them the pressure wave would have.
Continuity mistake: After McClane hits Targo with the chain and knocks him out, McClane searches him. Targo's body is not only in a different position, but the chain is wrapped around his head, which McClane never did.
Other mistake: When John and Zeus are being chased by the German guys in the car, John asks Zeus to pull out all the fuses in the fuse-box. The next shot is a quick shot of the speedometer etc. and it is lit up. Surely if all the fuses were out it wouldn't be lit?
Continuity mistake: In the car chase scene where the Germans are in the Dodge Ram and Zeus and John are in the car, during the mid point of that scene you'll notice the ram has a hood, and a few seconds later it is missing it.
Continuity mistake: While in the police station, a chubby guy brings the suitcase with the liquid bomb and to explain how it works he dips a stick with the liquid and throws it away to make it explode. Watch now the guy behind him covering his hears: Headset off, then he puts it on; then suddenly, in a very brief shot, when he is behind the chubby man, the headset is off again. In the next shots he has it on.
Revealing mistake: When Charlie (the bomb technician) hears that there are still children in the school, he continues trying to disarm the bomb. Pay attention to the shots of the countdown timer. It goes straight from 1:01 to 0:59. There is no 1:00.
Continuity mistake: In Harlem, when Zeus gets his arm cut by the black dude wielding the switchblade, another black dude is swinging the bottle toward McClane's head-with his left arm. The following scene, McClane gets his head injured from the same bottle wielded by the same dude-only this time wielded by his right arm not his left.
Continuity mistake: When the police van leaves McClane semi naked on the street, his beard is a mere shade. When he mets Zeus, 10 minutes later, his beard has grown much larger.
Continuity mistake: When the police get to Chester A. Arthur school and the kids are all in the auditorium, we see Detective Lambert walk into the auditorium wearing no badge in his jacket pocket. In the very next shot, he is wearing it again.
Continuity mistake: There is a big stain of wet blood on the back of Zeus just after McClane burns the cuffs to escape from the bomb on the ship. When they run outside the stain is dry, smaller and blurry.
Revealing mistake: When Simon is in the helicopter and shoots at McClane, check the metal strips next to his feet and the protruding metal parts where the squibs have been placed to allow for the pyrotechnics. It's particularly noticeable in the aerial shots where they couldn't quite be painted to match the asphalt parking lot.
Deliberate mistake: When McLane pulls out the phone he shot up after he and Zeus get into the Yugo there are a lot of coloured long curly cables hanging from the damaged phone. Mobile phones of this era would not have had any of these cables inside them, it is a deliberately made prop.
Suggested correction: No, the car would interpret missing fuses as blown fuses and would display a light to highlight the error.
GalahadFairlight
In German cars, the lid of the fuse box shows a table listing the purpose of each fuse. The engine control unit, fuel pump and the dashboard also have fuses that you should avoid to pull.
If he really pulled out all the fuses, the dashboard would be out of power and therefore dark. But maybe he didn't.